%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN216-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:17:00 AM UTC 2026
% Result : Unsatisfiable 238.61s 140.49s
% Output : Refutation 238.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 296 ( 61 ~; 55 |; 0 &; 180 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 0 ^; 83 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(l2_decl,type,
l2: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(m0_decl,type,
m0: $i > $i > $i > $o ).
thf(s1_decl,type,
s1: $i > $o ).
thf(p0_decl,type,
p0: $i > $i > $o ).
thf(d_decl,type,
d: $i ).
thf(q0_decl,type,
q0: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(75,axiom,
! [A: $i] : ( A @ ( b @ p0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(507,plain,
! [A: $i] : ( A @ ( b @ p0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(338,axiom,
a @ ( a @ ( b @ m0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(1009,plain,
a @ ( a @ ( b @ m0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ m0 ) ) )
| ~ ( C @ s1 )
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_133) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ m0 ) ) )
| ~ ( C @ s1 )
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1017,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ m0 ) ) )
| ~ ( C @ s1 )
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(cnf,[status(esa)],[1016]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
thf(380,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(381,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
inference(cnf,[status(esa)],[380]) ).
thf(1207,plain,
! [B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) )
| ~ $true
| ( B @ s1 ) ),
inference(paramod_ordered,[status(thm)],[507,381]) ).
thf(1208,plain,
! [B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) )
| ( B @ s1 ) ),
inference(simp,[status(thm)],[1207]) ).
thf(1209,plain,
b @ s1,
inference(pattern_uni,[status(thm)],[1208:[bind(A,$thf( b )),bind(B,$thf( b ))]]) ).
thf(55,axiom,
b @ ( d @ q0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(470,plain,
b @ ( d @ q0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ s1 )
| ~ ( B @ ( A @ q0 ) )
| ( A @ s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ s1 )
| ~ ( B @ ( A @ q0 ) )
| ( A @ s1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ s1 )
| ~ ( B @ ( A @ q0 ) )
| ( A @ s1 ) ),
inference(cnf,[status(esa)],[844]) ).
thf(28106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( d @ q0 ) )
!= ( B @ ( A @ q0 ) ) )
| ~ ( C @ s1 )
| ~ $true
| ( A @ s1 ) ),
inference(paramod_ordered,[status(thm)],[470,845]) ).
thf(28107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( d @ q0 ) )
!= ( B @ ( A @ q0 ) ) )
| ~ ( C @ s1 )
| ( A @ s1 ) ),
inference(simp,[status(thm)],[28106]) ).
thf(28108,plain,
! [A: $i] :
( ~ ( A @ s1 )
| ( d @ s1 ) ),
inference(pattern_uni,[status(thm)],[28107:[bind(A,$thf( d )),bind(B,$thf( b ))]]) ).
thf(28116,plain,
! [A: $i] :
( ~ ( A @ s1 )
| ( d @ s1 ) ),
inference(simp,[status(thm)],[28108]) ).
thf(28551,plain,
! [A: $i] :
( ( ( b @ s1 )
!= ( A @ s1 ) )
| ~ $true
| ( d @ s1 ) ),
inference(paramod_ordered,[status(thm)],[1209,28116]) ).
thf(28552,plain,
! [A: $i] :
( ( ( b @ s1 )
!= ( A @ s1 ) )
| ( d @ s1 ) ),
inference(simp,[status(thm)],[28551]) ).
thf(28553,plain,
d @ s1,
inference(pattern_uni,[status(thm)],[28552:[bind(A,$thf( b ))]]) ).
thf(237,axiom,
! [A: $i] : ( d @ ( A @ q0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(816,plain,
! [A: $i] : ( d @ ( A @ q0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(28094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( d @ ( A @ q0 ) )
!= ( C @ ( B @ q0 ) ) )
| ~ ( D @ s1 )
| ~ $true
| ( B @ s1 ) ),
inference(paramod_ordered,[status(thm)],[816,845]) ).
thf(28095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( d @ ( A @ q0 ) )
!= ( C @ ( B @ q0 ) ) )
| ~ ( D @ s1 )
| ( B @ s1 ) ),
inference(simp,[status(thm)],[28094]) ).
thf(28096,plain,
! [B: $i,A: $i] :
( ~ ( B @ s1 )
| ( A @ s1 ) ),
inference(pattern_uni,[status(thm)],[28095:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( d ))]]) ).
thf(28112,plain,
! [B: $i,A: $i] :
( ~ ( B @ s1 )
| ( A @ s1 ) ),
inference(simp,[status(thm)],[28096]) ).
thf(28927,plain,
! [B: $i,A: $i] :
( ( ( d @ s1 )
!= ( B @ s1 ) )
| ~ $true
| ( A @ s1 ) ),
inference(paramod_ordered,[status(thm)],[28553,28112]) ).
thf(28928,plain,
! [B: $i,A: $i] :
( ( ( d @ s1 )
!= ( B @ s1 ) )
| ( A @ s1 ) ),
inference(simp,[status(thm)],[28927]) ).
thf(28929,plain,
! [A: $i] : ( A @ s1 ),
inference(pattern_uni,[status(thm)],[28928:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(43090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ m0 ) ) )
| ~ $true
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(rewrite,[status(thm)],[1017,28929]) ).
thf(43091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ m0 ) ) )
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(simp,[status(thm)],[43090]) ).
thf(43118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( b @ m0 ) ) )
!= ( A @ ( C @ ( D @ m0 ) ) ) )
| ~ $true
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(paramod_ordered,[status(thm)],[1009,43091]) ).
thf(43119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( b @ m0 ) ) )
!= ( A @ ( C @ ( D @ m0 ) ) ) )
| ~ ( B @ ( B @ p0 ) )
| ( A @ ( A @ l2 ) ) ),
inference(simp,[status(thm)],[43118]) ).
thf(43120,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( a @ ( a @ l2 ) ) ),
inference(pattern_uni,[status(thm)],[43119:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( b ))]]) ).
thf(43122,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( a @ ( a @ l2 ) ) ),
inference(simp,[status(thm)],[43120]) ).
thf(1,negated_conjecture,
~ ( a @ ( a @ l2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
~ ( a @ ( a @ l2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
~ ( a @ ( a @ l2 ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(84433,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| $false ),
inference(rewrite,[status(thm)],[43122,371]) ).
thf(84434,plain,
! [A: $i] :
~ ( A @ ( A @ p0 ) ),
inference(simp,[status(thm)],[84433]) ).
thf(84435,plain,
! [B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[507,84434]) ).
thf(84436,plain,
! [B: $i,A: $i] :
( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) ),
inference(simp,[status(thm)],[84435]) ).
thf(84437,plain,
$false,
inference(pattern_uni,[status(thm)],[84436:[bind(A,$thf( b )),bind(B,$thf( b ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN216-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 17:26:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.22 % [INFO] Parsing done (247ms).
% 1.61/1.23 % [INFO] Running in sequential loop mode.
% 2.36/1.44 % [INFO] eprover registered as external prover.
% 2.36/1.44 % [INFO] Scanning for conjecture ...
% 2.76/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 368 axioms. Running axiom selection ...
% 3.18/1.65 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 4.11/1.80 % [INFO] Problem is propositional (TPTP CNF).
% 4.11/1.81 % [INFO] Type checking passed.
% 4.11/1.81 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 238.61/140.48 % [INFO] Killing All external provers ...
% 238.61/140.49 % Time passed: 139945ms (effective reasoning time: 139249ms)
% 238.61/140.49 % Axioms used in derivation (7): rule_125, axiom_38, rule_126, axiom_29, axiom_14, axiom_17, rule_133
% 238.61/140.49 % No. of inferences in proof: 48
% 238.61/140.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 139945 ms resp. 139249 ms w/o parsing
% 238.84/140.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 238.84/140.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------